The measurement of substances at extremely low concentrations in complex samples has absorbed the efforts of chemists for centuries. Modern spectroscopic techniques, which allow measurement of substances at parts-per-million (ppm) or even parts-per-billion (ppb) concentrations, have revolutionized this field and allowed the detection and measurement of naturally-occurring materials such as hormones, contaminating substances such as mercury, and pollutants such as atmospheric sulfur dioxide at levels far below those achieved using earlier methods of analysis. The direct measurement of many important substances in human tissue, however, has not been as successfully accomplished, and many other measurements where the substance to be measured is at a low concentration cannot be made accurately in a high noise and/or high clutter environment. One particularly challenging problem concerns the management of diabetes.
Diabetes is a condition in which the body's natural control of blood sugar (glucose) has been lost. Insulin is a hormone that is secreted by the pancreas that works with the body to process blood sugar. Typically, diabetes is caused by some problem with the body's ability to create or use insulin. Diabetes occurs in different medical conditions: type 1 diabetes (previously known as “juvenile diabetes”), type 2 (“adult onset”) diabetes, and gestational diabetes (a complication of pregnancy). In type 1 diabetes, the patient's pancreas is no longer able to produce insulin at normal rates, while in type 2 and gestational diabetes, a patient's cells are not able to properly utilize insulin. Some patients with type 2 or gestational diabetes can treat their conditions using diet, exercise, or a variety of pharmaceutical preparations. All patients with type 1 diabetes (and many with type 2, especially of longer duration) typically must control the disease with injections or infusions of insulin.
A body's normal creation and processing of insulin generally varies over the course of the day depending on a variety of factors, including when and what a person eats, whether that person is exercising, and the time of day. This variation in normal insulin production usually serves to maintain safe glucose levels in the body. If diabetes is left untreated, the complications that can arise can be extremely serious. In the absence of insulin, glucose in the blood can reach dangerously high levels. Extended periods of high blood glucose levels (“hyperglycemia”) can lead to a condition known as ketoacidosis, which, if untreated, can be fatal. Chronic poor control of glucose levels can also cause serious long-term complications, which include eye damage (resulting in blindness), kidney damage, cardiovascular disease, loss of feeling in the extremities, and slow healing of wounds. Frequently, diabetes may require amputations of toes, feet or legs. If blood glucose levels are allowed to drop below a threshold value (generally 50-60 milligrams per deciliter), the person can be in acute danger from this “hypoglycemia,” which can cause confusion, difficulty speaking, unconsciousness, and coma.
To allow better information and control, blood glucose measurement systems that can be used by individual users have been developed. These blood glucose measurement systems typically require the use of an electronic meter and disposable test strips. A test strip is inserted into the meter, and the user pricks himself or herself (usually on a finger) with a lancet to draw a small amount of blood which is applied to the test strip. The blood glucose meter, using one of a variety of analysis techniques, determines the amount of glucose in the small blood sample drawn from the user. However, because of the pain involved in lancing a body part to draw blood, the need to dispose of materials contaminated with blood, and the visibility and potential embarrassment of testing using conventional blood glucose monitoring systems, many investigators have tried to develop technologies that allow measurement of blood glucose without drawing blood or causing discomfort. These technologies have been termed “noninvasive” blood glucose measurement systems, or simply “noninvasive glucose.”
For example, U.S. Pat. No. 4,655,225, issued to Dähne et al., with a filing date of Apr. 18, 1985, appears to describe a relatively simple approach to measuring glucose in tissue. This patent states at column 1, lines 8 through 18: “This determination is carried out by measuring the optical near infrared absorption of glucose in regions of the spectrum where typical glucose absorption bands exist and computing the measured values with reference values obtained from regions of the spectrum where glucose has no or little absorption and where the errors due to background absorptions by the constituents of the surrounding tissues or blood containing the glucose are of reduced significance or can be quantitatively compensated.” When investigators eventually determined that no regions of the near-infrared NIR spectrum meeting these criteria could be found, they employed advanced techniques, augmented with sophisticated modifications to the instrumentation and complicated mathematical treatments. The NIR region used in these techniques is typically the region of the electromagnetic spectrum in the wavelength range of 700-2,500 nanometers
The most commonly-investigated technique for noninvasive glucose over the past twenty-five years or so has been near-infrared spectroscopy (NIRS), using light that is just beyond the visible portion of the spectrum, and generally considered to be a wavelength range of about 700 nanometers to about 2,500 nanometers. When near-infrared light is applied to tissue, generally the light is both scattered by cells and structures under the skin and is absorbed by substances in the tissue, including glucose, which can be termed an “analyte” (a substance whose concentration is being determined). The amount of absorbance due to glucose in this wavelength region, however, is extremely small and, coupled with (i) the low concentration of glucose in the fluids of tissue (about 50-500 milligrams per deciliter, equivalent to about 0.05% to 0.5%), (ii) the presence of many compounds with similar chemical structures and similar absorbance patterns in the near-infrared region, and (iii) the extremely high concentration of water in tissue, makes direct measurement of an analyte in this region of the spectrum very challenging, requiring the use of sophisticated spectroscopic imaging and computational techniques.
Many patents, such as U.S. Pat. No. 5,460,177, issued to Purdy, et al. in 1995, appears to describe approaches for using light from the near-infrared portion of the spectrum to provide “expressions” or spectra that can be examined to determine the concentration of glucose without drawing a sample of blood. Commonly-employed data reduction techniques in previous investigations generally include what are known as “multivariate” techniques, such as principal component analysis (“PCA”), partial least squares (“PLS”), support vector machine (“SVM”), and multiple linear regression (“MLR”). As a group, when these approaches are applied to the measurement of chemical substances, they are often referred to as “chemometrics.” These multivariate techniques may make it theoretically possible to create a correlation between measurable properties of a material like tissue, such as the amount of light absorbed or reflected as a function of wavelength (known as a “spectrum”), and the concentration of an analyte such as glucose. An example spectrum, which plots a variable related to light intensity (such as absorbance, transmittance, energy, etc.) as a function of the wavelength of light expressed in nanometers, is shown in FIG. 1.
In order to perform a multivariate analysis on a set of data, some techniques first build what is called a “model.” This may be done by first creating a number of like measurements (typically termed the “calibration set” in the context of multivariate analysis), which are spectra which contain the value of a parameter related to light intensity as a function of wavelength and which have known values for the concentration of the analyte. FIG. 2, for example, depicts an absorbance spectrum for one known concentration of glucose. The overall variance in the calibration data set may be separated into “factors” which typically represent decreasing amounts of variance. This model, once created using the multivariate technique, may represent the contribution of a measurement at each wavelength to the concentration of the analyte. The values of the model at each wavelength are often termed “final regression coefficients.” At some wavelengths, the value is positive, which may mean that the measurement at that wavelength contributes actual value to the calculation of the concentration, while at other wavelengths the value is negative, which may indicate an amount to be subtracted in the concentration calculation.
Once such a model, an example of which is shown in FIG. 3, has been created, a spectrum with an unknown analyte concentration can be analyzed using that model. With reference to FIG. 4, this can be done by multiplying the value of the new spectrum at each wavelength by the value of the final regression coefficient of the model at the same wavelength, and adding up all the results of those multiplications to give an estimated value of the analyte. The accuracy of this estimated concentration value usually depends on many factors—among them: the number of spectra used in the calibration set, the number of multivariate “factors” used to construct the model, the accuracy of the measurement process for the spectra, the similarity of the instrumentation used to generate the spectra, and the strength of the measured parameter. The measured parameter in the examples described above is the amount of absorbance of glucose molecules at each of the wavelengths, which is quite weak, and which is hidden under the strong absorbance of other components of tissue; the absorbance spectra of some tissue components are shown in FIG. 5, but these spectra are normalized—they are not based on a uniform scale.
Attempts at making measurements of glucose in tissue using these techniques have been made, but to the present time, these efforts have not succeeded in producing clinically accurate results. Several systems have used near-infrared spectroscopy and multivariate analysis techniques, but to date, no system for noninvasive measurement of glucose using near-infrared spectroscopy appears to have gained regulatory approval or appears to have been marketed in the U.S. In addition to multivariate and many other regression techniques, other practitioners have sought to extract a glucose signal from near-infrared tissue spectroscopy data using other methods of data reduction. Examples of these include: subtractive techniques where the spectra of interfering substances are sequentially removed from a tissue spectrum, analysis of a number of equations with several unknowns, neural networks, model trees, genetic algorithms, chaotic networks (and many related approaches that can be classified as fast learning algorithms), and an optical method known as Kromoscopy (Appl. Opt. 2000 Sep. 1: 39(25):4715-20). Many other approaches to measuring glucose in tissue have also been attempted, and a book has been written on the subject: The Pursuit of Noninvasive Glucose: “Hunting the Deceitful Turkey” by John L. Smith, 4th Edition (Copyright 2015), the disclosure of which is incorporated herein by reference in its entirety. Like the multivariate techniques described above, these techniques have not succeeded in producing clinically accurate results for noninvasive measurement of glucose. A new inventive approach for the direct, noninvasive measurement of glucose in tissue, as well as other analytes of interest, is therefore required.
The term “collision” has been used in different fields and contexts. For example, in computer networking and telecommunications and during the execution of various algorithms processing data, data-packet collisions generally imply that two distinct pieces of data have the same hash value, checksum, fingerprint, or cryptographic digest. The hashing collisions typically allocate the same memory location to different data values. In the computational problem of determining the intersection of two or more computer animated objects, as encountered in simulations and/or video games, linear algebra and computational geometry methods (e.g., the axis-aligned bounding box method for an n-body collision described in Lin, Ming C (1993). “Efficient Collision Detection for Animation and Robotics (thesis)”. University of California, Berkeley), collision analysis techniques may be used to determine whether two animated objects would or have collided and the time of impact, and for post-collision trajectory estimation. Computational atomic physics, which introduced a class of stochastic algorithms, such as those used in game theory, molecular dynamics, social simulations, and econometrics, is inspired by techniques used in particle-field simulations. These techniques generally involve collisions of atomic and subatomic particles (such as those described in Sigurgeirsson et al. (2001), “Algorithms for Particle-Field Simulations with Collisions”, Journal of Computational Physics 172, 766-807) and algorithms used for calculating post-collision electron and positron scattering and excitation in atoms and ions, such as in non-perturbative close coupling approach.
Various methods inspired by the classical Boltzmann collision operator used in statistical physics or fluid simulations for describing the interaction between colliding particles in rarefied gas include Bobylev-Rjasanow's Integral Transform Method, Pareschi-Russo's Spectral Method, and Mouhot-Pareschi's method. These computational techniques typically exploit the fundamental properties of the Boltzmann binary collision operator (e.g., the Bhatnagar-Gross-Krook (BGK) operator described in P. L. Bhatnagar, E. P. Gross, M. Krook (1954). “A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems,” Physical Review 94 (3): 511-525) that are related to conservation of mass, momentum, and energy, to infer properties of the colliding entities. While the binary collision operator and its approximation have been used in computer simulations and modeling to infer properties of colliding entities, to date these techniques generally do not take into consideration the environment of the entities, such as noise, clutter from confounders, and ultra-weak magnitudes of signals associated with entities of interest.
Computational collision techniques, such as those described in Collision-Based Computing, Andrew Adamatzky, (Ed.), ISBN 978-1-4471-0129-1, generally appear to describe computer implementations of various collisions described above, such collisions between particles or collisions between physical entities. With reference to FIGS. 6-8B, collisions between two traveling waveforms can occur on a space-time grid or a grid in another Cartesian coordinate system. In general, the two traveling waveforms move toward each other along a straight line connecting their centers of mass, with each point of one discretized wavefront (102 in FIG. 6) engaging in a series of collision steps with a corresponding point of the other discretized waveform (104 in FIG. 6), with the result of each step being determined by a set of rules established at the line of collision LC (100 in FIG. 6). Those rules determine the mathematical result of collision interactions and the shape of the resulting symbolic waveforms. Following completion of these partial steps in a collision between two waveforms, two resulting waveforms (106, 108 in FIGS. 7A-7F) are typically produced. The two resulting waveforms: (i) may be completely unchanged (except for a phase shift or delay) relative to the colliding waveforms, as shown in FIG. 7F), (ii) may be deformed (as shown in FIG. 8A), or (iv) either or both waveforms may be essentially completely destroyed (as shown in FIG. 8B). The nature of change in each waveform as a result of the collision (which can also be described as the degree of “elasticity” of the collision) generally depends on the composition of the waveforms, the relative energy of each waveform, and the rules established at the collision line Lc. A “soliton” is an example of a waveform that does do not change its properties other than a delay or phase shift during the collision process.